Maurits Cornelis Escher was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics. Despite wide popular interest, for most of his life Escher was neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the late twentieth century, he became more widely appreciated, and in the twenty-first century he has been celebrated in exhibitions around the world.
Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon.
Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015.
Ideas from mathematics have been used as inspiration for fiber arts including quilt making, knitting, cross-stitch, crochet, embroidery and weaving. A wide range of mathematical concepts have been used as inspiration including topology, graph theory, number theory and algebra. Some techniques such as counted-thread embroidery are naturally geometrical; other kinds of textile provide a ready means for the colorful physical expression of mathematical concepts.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Doris J. Schattschneider is an American mathematician, a retired professor of mathematics at Moravian College. She is known for writing about tessellations and about the art of M. C. Escher, for helping Martin Gardner validate and popularize the pentagon tiling discoveries of amateur mathematician Marjorie Rice, and for co-directing with Eugene Klotz the project that developed The Geometer's Sketchpad.
Code of the Quipu is a book on the Inca system of recording numbers and other information by means of a quipu, a system of knotted strings. It was written by mathematician Marcia Ascher and anthropologist Robert Ascher, and published as Code of the Quipu: A Study in Media, Mathematics, and Culture by the University of Michigan Press in 1981. Dover Books republished it with corrections in 1997 as Mathematics of the Incas: Code of the Quipu. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
Introduction to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press.
Geometry From Africa: Mathematical and Educational Explorations is a book in ethnomathematics by Paulus Gerdes. It analyzes the mathematics behind geometric designs and patterns from multiple African cultures, and suggests ways of connecting this analysis with the mathematics curriculum. It was published in 1999 by the Mathematical Association of America, in their Classroom Resource Materials book series.
Regular Figures is a book on polyhedra and symmetric patterns, by Hungarian geometer László Fejes Tóth. It was published in 1964 by Pergamon in London and Macmillan in New York.
Incidence and Symmetry in Design and Architecture is a book on symmetry, graph theory, and their applications in architecture, aimed at architecture students. It was written by Jenny Baglivo and Jack E. Graver and published in 1983 by Cambridge University Press in their Cambridge Urban and Architectural Studies book series. It won an Alpha Sigma Nu Book Award in 1983, and has been recommended for undergraduate mathematics libraries by the Basic Library List Committee of the Mathematical Association of America.
The Symmetries of Things is a book on mathematical symmetry and the symmetries of geometric objects, aimed at audiences of multiple levels. It was written over the course of many years by John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss, and published in 2008 by A K Peters. Its critical reception was mixed, with some reviewers praising it for its accessible and thorough approach to its material and for its many inspiring illustrations, and others complaining about its inconsistent level of difficulty, overuse of neologisms, failure to adequately cite prior work, and technical errors.
Dichromatic symmetry, also referred to as antisymmetry, black-and-white symmetry, magnetic symmetry, counterchange symmetry or dichroic symmetry, is a symmetry operation which reverses an object to its opposite. A more precise definition is "operations of antisymmetry transform objects possessing two possible values of a given property from one value to the other." Dichromatic symmetry refers specifically to two-coloured symmetry; this can be extended to three or more colours in which case it is termed polychromatic symmetry. A general term for dichromatic and polychromatic symmetry is simply colour symmetry. Dichromatic symmetry is used to describe magnetic crystals and in other areas of physics, such as time reversal, which require two-valued symmetry operations.
Polychromatic symmetry is a colour symmetry which interchanges three or more colours in a symmetrical pattern. It is a natural extension of dichromatic symmetry. The coloured symmetry groups are derived by adding to the position coordinates (x and y in two dimensions, x, y and z in three dimensions) an extra coordinate, k, which takes three or more possible values (colours).
Tilings and patterns is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed.
Geometric symmetry is a book by mathematician E.H. Lockwood and design engineer R.H. Macmillan published by Cambridge University Press in 1978. The subject matter of the book is symmetry and geometry.
Symmetry aspects of M. C. Escher's periodic drawings is a book by crystallographer Caroline H. MacGillavry published for the International Union of Crystallography (IUCr) by Oosthoek in 1965. The book analyzes the symmetry of M. C. Escher's colored periodic drawings using the international crystallographic notation.
M. C. Escher: Visions of Symmetry is a book by mathematician Doris Schattschneider published by W. H. Freeman in 1990. The book analyzes the symmetry of M. C. Escher's colored periodic drawings and explains the methods he used to construct his artworks. Escher made extensive use of two-color and multi-color symmetry in his periodic drawings. The book contains more than 350 illustrations, half of which were never previously published.
Color and Symmetry is a book by Arthur L. Loeb published by Wiley Interscience in 1971. The author adopts an unconventional algorithmic approach to generating the line and plane groups based on the concept of "rotocenter". He then introduces the concept of two or more colors to derive all of the plane dichromatic symmetry groups and some of the polychromatic symmetry groups.
